IDEAS home Printed from https://ideas.repec.org/a/bla/mathfi/v10y2000i1p77-88.html
   My bibliography  Save this article

Approximating Large Diversified Portfolios

Author

Listed:
  • Norbert Hofmann
  • Eckhard Platen

Abstract

This paper considers a financial market with asset price dynamics modeled by a system of lognormal stochastic differential equations. A one‐dimensional stochastic differential equation for the approximate evolution of a large diversified portfolio formed by these assets is derived. This identifies the asymptotic dynamics of the portfolio as being a lognormal diffusion. Consequentially an efficient way for computing probabilities, derivative prices, and other quantities for the portfolio are obtained. Additionally, the asymptotic strong and weak orders of convergence with respect to the number of assets in the portfolio are determined.

Suggested Citation

  • Norbert Hofmann & Eckhard Platen, 2000. "Approximating Large Diversified Portfolios," Mathematical Finance, Wiley Blackwell, vol. 10(1), pages 77-88, January.
    • Handle: RePEc:bla:mathfi:v:10:y:2000:i:1:p:77-88
    DOI: 10.1111/1467-9965.00081
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/1467-9965.00081
    Download Restriction: no
    File URL: https://libkey.io/10.1111/1467-9965.00081?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Herbertsson, Alexander, 2023. "Saddlepoint approximations for credit portfolio distributions with applications in equity risk management," Working Papers in Economics 839, University of Gothenburg, Department of Economics.
    2. Truc Le & Eckhard Platen, 2006. "Approximating the Growth Optimal Portfolio with a Diversified World Stock Index," Research Paper Series 180, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Eckhard Platen & Renata Rendek, 2009. "Simulation of Diversified Portfolios in a Continuous Financial Market," Research Paper Series 264, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Herbertsson, Alexander, 2023. "Risk management of stock portfolios with jumps at exogenous default events," Working Papers in Economics 836, University of Gothenburg, Department of Economics.
    5. Olivier Le Courtois, 2022. "On the Diversification of Fixed Income Assets," Risks, MDPI, vol. 10(2), pages 1-21, February.
    6. Mirela NICHITA, 2015. "An Overview On State Of Knowledge Of Risk And Risk Management In Economics Fields," SEA - Practical Application of Science, Romanian Foundation for Business Intelligence, Editorial Department, issue 7, pages 423-430, April.
    7. Eckhard Platen, 2004. "Diversified Portfolios with Jumps in a Benchmark Framework," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(1), pages 1-22, March.
    8. Lim Kian Guan & Liu Xiaoqing & Tsui Kai Chong, 2004. "Asymptotic dynamics and value-at-risk of large diversified portfolios in a jump-diffusion market," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 129-139.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bla:mathfi:v:10:y:2000:i:1:p:77-88. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0960-1627 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.